﻿468 Messrs. C- G. Darwin and R. H. Fowler on 



(1 — 2 6 )~ M (1— ^) -N , so CE A 2 is easily seen to be given 



by operating with (~^) in the same way. Thus 



ce?= ^[% { («£) Wr- } (i-^)-*. 



If we again suppose an infinite bath of temperature $, we 

 can omit the second term of the asymptotic expansion (6'2) 

 and obtain 



e>(i_*O m {(^) 2 (i-*T m }, 



=(i-y) M ^{A(i-*r*b 



— <^7 



and so the fluctuation is 



(E A -E A )*=E7-(E A )* 



-iKP ^ 



(8-5) 



J 



This is a result of which Einstein * made use in his work 

 on fluctuations of radiation. It should be emphasized that 

 these results are only accurate in a temperature bath, and 

 not when the number of systems A is a finite fraction of the 

 assembly. 



In all cases (6*2) shows that the possession of E A is a 

 norma! property of the assembly. 



If we work out exactly the second terms in the asymptotic 

 formulse of § 6 and apply them to the fluctuations of a r and 

 E A we find 



(a r -a,)'-a r [l- g |l+ ^ E /cft J J' < 8 6 > 



^^-^^^fV^f) • • • <*?> 



Formula (4*6) above is a special case of (8*6). 



* A. Einstein, Phys. Zeitschr. vol. x. p. 185 (1909). 



